text:
\section{Introduction}\label{sec:intro}

Let $\mathcal F$ be any family of graphs. Given a graph $G$, a subset
$X\subseteq V(G)$ is called a \emph{transversal} (of $\mathcal F$) if the graph
$G-X$ obtained by deleting $X$ does not contain any member of $\mathcal F$. We
say that $\mathcal{F}$ has the \emph{Erd\H{o}s-P\'osa property} if there exists
a function $f\colon\mathbb{N}\to \mathbb R$ such that every graph $G$ which
does not contain $k$ vertex-disjoint members of $\mathcal{F}$ contains a
transversal of size at most $f(k)$.

The study of this property dates back to 1965 when Erd\H{o}s and P\'osa
\cite{erdos65} showed the following:

\begin{theorem*}\label{thm:erdos-posa}
  Every graph contains either $k$ vertex-disjoint cycles or a set of
  at most $f(k) = (4 + o(1)) k \log k$ vertices meeting all its cycles.
\end{theorem*}

The value of $f(k)$ in this theorem is optimal up to the constant factors. The
Erd\H{o}s-P\'osa{} property is closely related to classical `covering vs.\ packing'
results in graph theory, such as K\H{o}nig's theorem or Menger's theorem. For
example, K\H{o}nig's theorem can be stated as follows: every bipartite graph contains
either $k$ vertex-disjoint edges or a set of $f(k)=k$ vertices meeting all the
edges. The above result has spawned a long line of papers about the
duality between packing and covering of different families of graphs, directed
graphs, hypergraphs, rooted graphs, and other combinatorial objects (see a
recent survey of Raymond and Thilikos \cite{2016survey} for more information).

In this paper, we are interested in the Erd\H{o}s-P\'osa property for the
family $\mathcal F_l = \{C_m \mid m \geq l\}$ of cycles of length at least $l$.
A 1988 result of Thomassen~\cite{thomassen88} implies that for every $l$, the
family $\mathcal F_l$ has the Erd\H{o}s-P\'osa property with a function $f(l,
k)\in 2^{l^{\mathcal O(k)}}$ (though recent results of Chekuri and Chuzhoy make
it possible to substantially improve the dependency on $k$ in this
bound~\cite{chekuri13}). This result was sharpened by Birmel\'e, Bondy, and
Reed~\cite{bondy07} to $f(l, k) \in \mathcal{O}(lk^2)$ in 2007 and by Fiorini
and Herinckx~\cite{fiorini14} to $f(l, k) \in \mathcal{O}(lk\log k)$ in 2014.
In this paper we improve these results to the asymptotically optimal bound
$f(l, k)\in \mathcal O(kl+k\log k)$, thus settling the question asked
in~\cite{bondy07} and~\cite{fiorini14}.

\begin{theorem}\label{thm:main}
  For every integer $l \ge 3$, the family $\mathcal{F}_l$
  of cycles of length at least $l$ has the Erd\H{o}s-P\'osa
  property with the function
  \[ f(l, k) = \begin{cases}
    6kl + 10k\log_2 k + 40k + 10k\log_2\log_2 k &\text{if }k\geq 2,\\
    0 & \text{if }k=1.
  \end{cases} \]
\end{theorem}

Certainly the constant factors in Theorem~\ref{thm:main} are not
optimal. Birmel\'e, Bondy, and Reed~\cite{bondy07} conjectured the
correct function in the case $k=2$ to be $f(l, 2) = l$. The complete graph on
$2l-1$ vertices shows that, if true, this bound would be tight.
Lov\'asz~\cite{lovasz65} confirmed the conjecture for $l=3$, while
Birmel\'e~\cite{birmele03} confirmed the cases $l=4$ and $l=5$. For larger $l$,
Birmel\'e, Bondy, and Reed~\cite{bondy07} proved that the optimal function
satisfies $f(l, 2)\leq 2l+3$. This was recently improved by Meierling,
Rautenbach and Sasse~\cite{meierling14} to $f(l, 2)\leq 5l/3+29/2$.

There are two constructions which together imply that the function in
Theorem~\ref{thm:main} is asymptotically optimal for large $k$ and $l$. On the
one hand, for all $k$ and $l$ we must have $f(l, k) \geq (k-1)l$, as can be seen
from the example of a complete graph on $kl-1$ vertices: this graph does not contain $k$ vertex-disjoint
cycles of length at least $l$, but to remove all cycles of length at least $l$ one must
delete $kl-1 - (l-1)= (k-1)l$ vertices. This construction also gives the lower
bound $f(l, k) \geq \frac12(k-1) \log_2 k$ whenever $l \geq \frac12\log_2 k$.

On the other hand, for $l < \frac12\log_2 k$ we can obtain the lower bound
$f(l, k) \geq \frac18 k\log_2 k$ using the fact that there exist $3$-regular
graphs on $n$ vertices with girth at least $(1-o(1))\log_2 n$~\cite{erdos63}.
Indeed for $n$ large enough, let $G$ denote such a graph with girth $g(G)$.
Clearly $G$ contains at most $n/g(G)$ vertex disjoint cycles. So fix $k=\lfloor
n/g(G) \rfloor + 1>n/g(G)$ and observe that for $n$ large enough $n\geq \frac12 k
\log_2k$. All cycles in $G$ have length at least $g(n)>\frac{1}{2}\log_2 k>l$.
Thus if $X$ is a transversal of all cycles of length at least $l$ then $G-X$ is
a forest.  Because $G$ is $3$-regular, removing $|X|$ vertices leaves at least
$3n/2 -3|X|$ edges. Since the resulting graph should be a forest, we need
$\frac 32 n - 3|X| \le n - |X|$, and therefore every transversal must have size
$|X| \ge \frac n4\geq \frac18 k\log_2 k$. This gives the desired lower bound
$f(l,k) \geq \frac 18 k\log_2k$.

\paragraph{Notation}
All graphs are assumed to be simple unless stated otherwise. However,
multigraphs do make an appearance in the proof. We define a multigraph $M$ in
the standard way, that is, as an ordered pair $(V, E)$, where $V$ denotes the
vertex set of $M$ and $E$ is the multiset of edges of $M$. For a (multi-)graph
$G$ we denote by $V(G)$ and $E(G)$ the vertex set and the edge (multi-)set of $G$,
respectively. Given two multigraphs $M_1$ and $M_2$ we write $M_1\cup M_2$ for
the multigraph $M=(V,E)$ where $V = V(M_1) \cup V(M_2)$ and $E = E(M_1)\cup E(M_2)$.
In particular, the multiplicity of an edge $e$ in $M_1\cup M_2$ is equal to the
sum of multiplicities of $e$ in $M_1$ and $M_2$. We use the standard asymptotic
notation $\mathcal{O}$, $o$, $\omega$ and $\Omega$.

\paragraph{Tree-width}
Our results also imply an asymptotically optimal upper bound on the tree-width
$\tw(G)$ of every graph $G$ that does not contain $k$ vertex-disjoint cycles of
length at least $l$. We need the following theorem.

\begin{theorem}[Birmel\'e~\cite{birmele02}]\label{thm:birm}
  Suppose that $G$ does not contain a cycle of length at least $l$.
  Then $\tw(G) \leq l-2$.
\end{theorem}

Generalizing this, Birmel\'e, Bondy, and Reed proved
that any graph $G$ not containing $k$ vertex-disjoint cycles of length
at least $l$ has tree-width in $\mathcal O(k^2l)$~\cite{bondy07}.
Theorem~\ref{thm:main} allows us to improve this bound:

\begin{corollary}
  Assume that $G$ does not contain $k$ vertex-disjoint
  cycles of length at least $l$. Then

  $\tw(G) \in \mathcal O(kl + k\log k)$.
\end{corollary}
\begin{proof}
  Assume that $G$ does not contain $k$ vertex-disjoint cycles of length at least
  $l$. By Theorem~\ref{thm:main} there is a set $X\subseteq V(G)$ of size $|X|
  \leq 6kl + 10k\log_2 k+40k + 10\log_2\log_2 k$ such that $G-X$ does not
  contain a cycle of length at least $l$. By Theorem~\ref{thm:birm} we have
  $\tw(G-X)\leq l-2$. We can turn a tree-decomposition of $G-X$ into a
  tree-decomposition of $G$ by adding $X$ to each bag, which gives the bound
  $\tw(G) \leq \tw(G-X) + |X| \leq (6k+1)l+ 10k\log_2 k + 40k + 10\log_2\log_2
  k-2$.
\end{proof}

This is tight in the sense that there are examples of graphs that do not
contain $k$ disjoint cycles of length at least $l$ and whose tree-widths are in
$\Omega(kl+k\log k)$.

In fact, similar constructions as above work. An example where $\tw(G)\geq
kl-2$ is provided by the complete graph on $kl-1$ vertices. For $l \le c \log
k$, for sufficiently small positive constant $c$, we can use fact that there
exist constant-degree expander graphs $G$ on $n$ vertices with $g(G)\in
\Omega(\log n)$ and $\tw(G)\in \Omega(n)$ (using for example the results
in~\cite{lps88} and~\cite{bptw10}). Choosing $k$ such that $ k \cdot g(G) \in
[n+1, 2n]$ one obtains a graph which does not contain $k$ vertex-disjoint cycles
(of any length) but whose tree-width is in $\Omega(k\log k)$.

\section{Proof of the main result}\label{sec:proof}

We will use the following lemma.

\begin{lemma}[Diestel~\cite{diestel05}]\label{lem:cubic}
  For each natural number $k$, let
  \[ s_k := \begin{cases}4k(\log_2 k + \log_2\log_2 k + 4) &\text{if } k \ge 2, \\
    1& \text{if }k=1.
  \end{cases}
  \]
  Then every $3$-regular multigraph on at least $s_k$ vertices contains
  a set of $k$ vertex-disjoint cycles.
\end{lemma}

Fix $l\geq 3$ and a graph $G$. We say that a cycle in $G$ is \emph{long} if it has
length at least $l$, and otherwise we say that it is \emph{short}. By
\emph{disjoint}, we always mean \emph{vertex-disjoint}.
We assume that $G$ does not contain $k$ disjoint long cycles and
show that $G$ contains a transversal of $\mathcal F_l$
of size at most $f(l,k)$, where
\[ f(l,k) = \begin{cases}6kl + 10k\log_2 k + 40k + 10k\log_2\log_2 k &\text{if }k\geq 2,\\
  0 & \text{if }k=1.
\end{cases}\]
The proof is by induction on $k$, where the base case $k=1$ is obvious.

If $G$ contains a long cycle $C$ of length at most $6l$ then by induction,
$G-V(C)$ contains either $k-1$ disjoint long cycles or a transversal $X$ of
size $f(l,k-1)$. In the first case $G$ contains $k$ disjoint long cycles and in
the second case $X\cup V(C)$ is a transversal of size $f(l,k-1)+6l\leq f(l,k)$.
Therefore we may assume that every long cycle in $G$ contains strictly more
than $6l$ vertices.

Let $H$ denote a maximal subgraph of $G$ with the following properties:
\begin{enumerate}
  \item all vertices of $H$ have degree $2$ or $3$ in $H$;
  \item $H$ contains no short cycle.
\end{enumerate}
Similarly as in \cite{erdos65}, observe that $H$ is the union of a subdivision
of a $3$-regular multigraph and at most $k-1$ disjoint long cycles. If $H$
contains at least $s_k$ vertices of degree $3$ then by Lemma~\ref{lem:cubic},
it contains $k$ disjoint cycles, which by definition of $H$ are all long. So
from now on, we can assume that $H$ contains fewer than $s_k$ vertices of
degree $3$.

\begin{definition}
  We say that a path $P$ is an \emph{$H$-path} if its endpoints are distinct vertices of $H$ and
  if it is internally vertex-disjoint from $H$. Observe that we allow for
  $P\subseteq H$ if the length of $P$ is one. We say that $P$ is a \emph{proper
  $H$-path} if none of its edges are contained in $H$.
\end{definition}

For each $i\in\{2,3\}$ let $V_i\subseteq V(H)$ denote the set of vertices with
degree $i$ in $H$. We modify $G$ by removing all edges from $E(G)\setminus
E(H)$ that are incident to a vertex from $V_3$. Note that any transversal of
the modified graph can be turned into a transversal of the original graph by
additionally removing $V_3$. Furthermore $H$ is still maximal in the modified graph.  From
now on we assume that all vertices of $V_3$ have degree $3$ in $G$. In
particular the endpoints of every proper $H$-path lie in $V_2$.

This implies that every $H$-path has length at most $l$, as otherwise we could
add the path to $H$ without violating either the degree or the cycle condition,
contradicting the maximality. For the same reason, if $P$ is an $H$-path with
endpoints $s,t\in V(H)$, then there exists a path between $s$ and $t$ in $H$ of length
at most $l$. In fact, as $H$ contains no cycles of length at most $2l$, this
path is unique.
Thus the following notion is well-defined.

\begin{definition}[Projection]
  Suppose that $P$ is an $H$-path with endpoints $s, t\in V(H)$. The
  \emph{projection} of $P$, denoted by $\pi(P)$, is defined to be the unique
  path of length at most $l$ between $s$ and $t$ in $H$.

  Let $C \subseteq G$ be a cycle in $G$ that intersects $H$ in at least two
  vertices. We define the projection $\pi(C)$ of $C$ as follows. Let $C =
  P_1\cup \dotsc \cup P_m$ be a decomposition of $C$ into distinct $H$-paths.
  Then we define the projection of $C$ to be the multigraph $\pi(C) =
  \pi(P_1)\cup \dotsb \cup \pi(P_m)$.

  If $P$ is a path in $G$ with distinct endpoints in $H$ (not necessarily an
  $H$-path), then we define the projection analogously: let $P= P_1\cup \dotsb \cup P_m$
  be a decomposition into  $H$-paths and define $\pi(P) = \pi(P_1)\cup \dotsb
  \cup \pi(P_m)$.
\end{definition}

We remark that in the definition above, the decomposition of a cycle or path
into distinct $H$-paths is unique up to permutation, so that the projection is
in fact well-defined.

We claim that information about the length of a cycle can be recovered by
looking at the following property of its projection:
\begin{definition}
  A multigraph $M$ is called \emph{even} if the multiplicity of every edge in
  $M$ is even.
\end{definition}

\begin{lemma}\label{lemma:projection}
  Suppose that $C$ is a cycle in  $G$ which intersects $H$ in at least two vertices. If
  $V(\pi(C))$ induces a tree in $H$, then $C$ is short. If $\pi(C)$ is not
  even, then $C$ is long.

\end{lemma}

\begin{proof}
  Among all cycles for which the lemma fails, we may pick a cycle $C$ whose
  decomposition into $H$-paths minimizes the number of proper $H$-paths. If
  none of these $H$-paths is proper, then $C\subseteq H$ and thus $\pi(C)=C$ is not even and long.
  Therefore we may assume that $C$ contains at least one proper
  $H$-path $P$.

  Note that $\pi(P)$ is a path in $H$ with the same endpoints as $P$. If $C$
  contains all edges of $\pi(P)$, then we actually have $C=P\cup \pi(P)$ and so
  the projection of $C$ is even. Moreover,
  the length of  $C$ is $|P|+|\pi(P)|\leq 2l$. Since all long cycles have
  length greater than $6l$ we see that $C$ must be short and we are done.
  Therefore, we can assume that at least one edge of $\pi(P)$ does not belong
  to $C$. Since $\pi(P)$ is a path with endpoints in $V(C)$, there exists a
  path $P'\subseteq \pi(P)$ with endpoints $s,t\in C$ which is internally
  vertex-disjoint from $C$ and whose edges are not edges of $C$. Let $P_1, P_2
  \subseteq C$ denote the two internally disjoint $s,t$-paths in $C$ and
  consider the two cycles $C_1\coloneqq P_1\cup P'$ and $C_2\coloneqq P_2\cup
  P'$. Observe that since $\pi(P')\subseteq \pi(C)$ we have
  $V(\pi(C))=V(\pi(C_1))\cup V(\pi(C_2))$. Additionally, the parity of each
  edge in $\pi(C)$ is equal to the parity of the same edge in $\pi(C_1)\cup
  \pi(C_2)$.

  We are now ready to prove the first claim. Assume that $C$ is long and that
  $H[V(\pi(C))]$ is a tree. Then the projections of $C_1$ and $C_2$ induce
  trees as well and therefore both cycles contain at least one proper $H$-path.
  In particular both cycles contain strictly fewer proper $H$-paths than $C$.
  Furthermore, at least one of the two cycles has length at least $\abs C/2$.
  Since $C$ has length at least $6 l$, this cycle is still long, which
  contradicts the minimality of $C$.

  For the second claim, assume that $C$ is short and that $\pi(C)$ is
  not even. Observe that we have  $|C_i| \le |C| + |P'| \le l + |P'|$ for
  each $i\in\{1,2\}$. As $P'$ is a subgraph of $\pi(P)$ we know that $|C_i| \le
  2 l$, which implies that both cycles $C_i$ are short. Since $H$ contains only
  long cycles, this means that both $C_1$ and $C_2$ contain at least one proper
  $H$-path, so both $C_1$ and $C_2$ contain fewer proper $H$-paths than $C$.
  Finally, as $\pi(C)$ is not even and since each edge in $\pi(C_1)\cup \pi(C_2)$
  has the same parity as the same edge in $\pi(C)$, at least one of
  $\pi(C_1)$ and $\pi(C_2)$ is not even. This contradicts the minimality
  of $C$.
\end{proof}

\begin{definition}
  Let $X \subseteq V(H) \cup E(H)$ be a set of vertices and edges of $H$. Let
  us denote by $G - X$ and $H-X$ the graphs obtained by deleting from $G$ and
  $H$ the edges and vertices in $X$.

  Then we say that $X$ is \emph{$\pi$-preserving} if $P \subseteq G-X$ implies
  $\pi(P)\subseteq H-X$ for all $H$-paths $P$.
\end{definition}

The following lemma is the crucial
ingredient of the proof of Theorem \ref{thm:main}. For now, we only state the
lemma; the proof is given in the next subsection.

\begin{lemma}\label{lemma:forest-cut}
  There exists a $\pi$-preserving set $X$ for which $H-X$ is a forest and such
  that $|X \cap (V_2\cup E(H[V_2]))| \leq 3|V_3|/2+k$.
\end{lemma}

We can now finish the proof of Theorem~\ref{thm:main}. By the lemma, there exists a
$\pi$-preserving set  $X$ for which $H-X$ is a forest and such that
$|X\cap (V_2\cup E(H[V_2]))|\leq 3|V_3|/2+k$. Suppose that $C$ is a cycle that intersects
$H$ at least twice. Then because $X$ is $\pi$-preserving, we know in
particular that all vertices of $V(\pi(C))$ are contained in the same component
of $H-X$. Since each component of $H-X$ is a tree, the graph $H[V(\pi(C))]$
must also be a tree. Thus, by Lemma~\ref{lemma:projection}, the cycle $C$ is
short. It follows that every long cycle in $G-X$ intersects $H$ at most once.

To construct the transversal we define the following two sets.
\begin{enumerate}
  \item Let $X'\subseteq V(H)$ be a set containing the vertices in $X\cap V_2$ and also
    containing one endpoint of each edge in $X\cap E(H[V_2])$.
  \item Let $Z\subseteq V(H)$ denote the set of all vertices $z\in V(H)$ for
    which there exists some long cycle $C_z$ such that $V(C_z)\cap
    V(H)=\left\{z\right\}$.
\end{enumerate}

We now claim that $V_3\cup X'\cup Z$ is a transversal of all long cycles. Every long
cycle $C$ intersects $H$ at least once since otherwise $C$ could be added to
$H$. If $C$ intersects $H$ exactly once than it intersects $Z$. If $C$
intersects $H$ at least twice then, by the observation above, this means that
$C$ intersects $X$. But then $C$ must intersect either $V_3$ or $X'$. So
$V_3\cup X'\cup Z$ is a transversal in $G$. Recall that in the beginning, we
modified the graph $G$ by removing all edges of $E(G)\setminus E(H)$ that are
incident to a vertex of $V_3$. Since we remove $V_3$ anyway, $V_3\cup X'\cup Z$
is also a transversal in the original graph.

It remains to bound the size of this transversal. If for some $z\neq z'\in Z$
the cycles $C_z$, $C_{z'}$ intersect, then one can see that the assumption
$|C_z|,|C_{z'}| \geq 6l$ implies that $C_z\cup C_{z'}$ contains a $z$-$z'$-path
of length at least $l$, which contradicts the fact that there are no $H$-paths
of length $l$ or longer. Therefore $\left\{C_z\mid z\in Z\right\}$ is a
collection of vertex disjoint long cycles and in particular $\abs{Z} < k$.
Furthermore, we have $|X'| \leq 3|V_3|/2+k$. Since $|V_3|< s_k$, we get \[
|V_3\cup X'\cup Z| < |V_3| + \frac32|V_3| + 2k < \frac52s_k + 2k \leq f(l,k).
\] This completes the proof of Theorem~\ref{thm:main}. However, we still need
to prove Lemma~\ref{lemma:forest-cut}.

\subsection{Proof of Lemma \ref{lemma:forest-cut} }

Let us call a $\pi$-preserving set \emph{valid} if it contains at most one
edge or vertex from every component of $H[V_2]$.
There exists at least one valid $\pi$-preserving set: the empty set. Let $X$
denote a $\pi$-preserving set of maximal size. Since $H$ is the disjoint union
of a subdivision of a $3$-regular graph on $|V_3|$ vertices and fewer than
$k$ cycles, the fact that $X$ is valid immediately implies that $|X\cap (V_2\cup E(H[V_2]))| \leq
3|V_3|/2 + k$. We will show that $H-X$ is a forest. Assume
towards a contradiction that $H-X$ contains a cycle. Among all such cycles let
$C=(x_0\dots,x_n)$ denote one of minimum length. Since $H$ only contains long cycles, we
have $|C|>6l$. Let $B_{H-X}(C,l)$ denote the ball of radius $l$ around $C$ in
$H-X$, i.e., the set of vertices that have distance at most $l$ to a vertex of
$C$ in $H-X$. Let $H_C$ be the subgraph of $H-X$ induced by $B_{H-X}(C,l)$. We
now have some claims about the structure of $H_C$. First of all, it is clear
that $C\subseteq H_C$. Moreover:

\begin{claim}\label{claim:1}
  In $H_C$, every vertex $v$ has a unique nearest vertex in $C$ (which may be
  $v$ itself if $v\in V(C)$).
\end{claim}
\begin{proof}
  This is clear if $v\in V(C)$, so assume otherwise. By the definition of
  $H_C$, the distance from $v$ to any nearest vertex on $C$ is at most $l$.
  If there are two nearest vertices of $v$ on $C$, then using the shortest
  path between them on $C$, we obtain a cycle
  of length at most $|C|/2 +2l < |C|$ in $H_C$, where the inequality follows from $|C|>4l$. But
  this would contradict the minimimality of $C$.
\end{proof}

This claim shows in particular that the projection map $p\colon V(H_C)\to V(C)$
taking vertices of $H_C$ to their unique nearest vertex in $C$ is well-defined.
In fact, the preimages of this projection have rather nice properties:

\begin{claim}\label{claim:structure}
  The following hold:
  \begin{enumerate}[(i)]
    \item for every $x\in V(C)$, the graph $H_C[p^{-1}(x)]$ is a tree;
    \item for distinct vertices $x,y\in C$, there are no edges between $p^{-1}(x)$
      and $p^{-1}(y)$ in $H_C\setminus C$;
  \end{enumerate}
\end{claim}
\begin{proof}
  For (i) simply observe that the diameter of $H_C[p^{-1}(x)]$ is at most $2l$, so
  any cycle would be of length at most $4l$; however $H$ does not contain cycles that are this short.
  The argument for (ii) is similar to the argument in the proof of Claim~\ref{claim:1}: if such
  an edge exists, then $H_C$ contains a cycle of length at most $|C|/2+2l+1 < |C|$, using
  $|C|>6l > 4l+2$. This would contradict the minimality of $C$.
\end{proof}

By the above claim, the graph $H_C$ is just the cycle $C$ with
trees attached at every vertex. In particular, $H_C-e$ is a tree for any edge $e\in E(C)$.

We will now construct a larger graph $G_C$ where $H_C\subseteq G_C\subseteq G-X$ as follows.
Let $D = \{x_l,x_{l+1},\dotsc,x_{n-l}\}$.
For each $x\in D$, let $P(x)$ be the set of all $H$-paths $P$ in $G-X$ such
that $x \in V(\pi(P))$.  Since $X$ is $\pi$-preserving, every such path satisfies
$\pi(P)\subseteq H-X$. We then define
\[ G_C = H_C \cup \bigcup_{x\in D} P(x). \]
It is worth noting that $G_C \cap H = H_C$.
Let us further denote by $e^*$ the edge $\{x_0, x_n\}$.
We have the following very important claim, whose proof we postpone to the end of the section.

\begin{claim}\label{claim:obvious}
For every proper $H$-path $P\subseteq G_C$, we have $\pi(P)\subseteq H_C-e^*$.
  In particular, every path in $G_C-e^*$ with endpoints in $V(H_C)$ projects
  to a subgraph of $H_C-e^*$.
\end{claim}

Using the claim, we can now finish the proof of Lemma~\ref{lemma:forest-cut}.
Let $A=\left\{x_0,\dots,x_l\right\}$ and
$B=\left\{x_{n-l},\dots,x_n\right\}$. We claim that $G_C-e^*$ does not contain
two internally disjoint $A$-$B$-paths. Suppose for a contradiction that $P_1$
and $P_2$ are two such paths, where we can assume that both $P_1$ and $P_2$
intersect both $A$ and $B$ in exactly one vertex. By Claim~\ref{claim:obvious}
both paths project onto a subgraph of $H_C-e^*$, which implies in particular
that $\pi(P_1)\cup \pi(P_2)$ does not contain $e^*$. We can combine $P_1$ and
$P_2$ into a cycle in $G_C-e^*$ by adding the shortest paths between the
endpoints of $P_1$ and $P_2$ in $C[A]$ and $C[B]$, respectively. The projection
of this cycle lies in $H_C-e^*$ which is a tree. Thus, by
Lemma~\ref{lemma:projection}, this cycle is short. In particular we have $|P_1|
< l$. However, as the projection of $P_1$ avoids $e^*$, connecting the
endpoints of $P_1$ using the shortest path in $C[A\cup B]$ results in a cycle
$C_1$ whose projection is not even, since the multiplicity of $e^*$ in
$\pi(C_1)$ is one. So by Lemma \ref{lemma:projection} the cycle $C_1$ is long.
Since any path in $C[A\cup B]$ is of length at most $2l+1$,  the length of
$C_1$ is bounded by $\abs {P_1} + 2l+1 \leq 3l$. This is a contradiction since
$G$ does not contain a long cycle of length at most $3l$. We conclude that
there are no two internally disjoint $A$-$B$-paths in $G_C-e^*$.

By Menger's theorem, $G_C-e^*$ contains a single-vertex $A$-$B$-cut. Denote the
cut vertex by $x$. Because $C$ contains an $A$-$B$-path from $x_l$ to
$x_{n-l}$, we must have $x\in D$. Thus $x$ has degree at least two in $H_C-e^*$.
We distinguish two cases, depending on whether $x$ has degree two or three in
$H_C-e^*$.

First, assume that $x$ is a vertex of degree two in $H_C-e^*$. By the
maximality of $X$, we know that $X\cup \{x\}$ is not a valid $\pi$-preserving
set. One possibility is that $X\cup \{x\}$ is $\pi$-preserving, but it
is not valid. Since $X$ is valid on its own, this means that $x$ belongs to a
component of $H[V_2]$ which intersects $X$. But since $x$ belongs to the cycle
$C\subseteq H-X$, this is impossible. Thus it must be that $X\cup \{x\}$ is not
a $\pi$-preserving set. Since $X$ by itself is $\pi$-preserving, the definition
implies that there exists an $H$-path $P$ in $G-X$ such that $x \in V(\pi(P))$
and $x \notin V(P)$. Note that $P\subseteq G_C-e^*$ by the definition of $G_C$.
Since $x$ has degree two in $H_C-e^*$ and since $H_C-e^*$ is a tree, we know
that $H_C-e^* - x$ breaks into exactly two trees $T_1$ and $T_2$. As $x \in
V(\pi(P))$ and $\pi(P)\subseteq H_C-e^*$, it must be that $P$ has one endpoint
in $T_1$ and the other in $T_2$. It follows that $T_1 \cup T_2 \cup P$ is a
connected graph and thus $T_1 \cup T_2 \cup P$ must contain an $A$-$B$-path.
This is a contradiction with the fact that $x$ separates $A$ and $B$ in
$G_C-e^*$ and completes the proof in this case.

Next, assume that $x$ is a vertex of degree three in $H_C-e^*$. Recall
that then $x$ has degree $3$ in $G$ as well, and in particular no proper
$H$-path has $x$ as an endpoint. As in the previous case, $H_C -e^*- x$ breaks
into exactly three trees $T_1, T_2$ and $T_3$. Let $x^-$ and $x^+$ be the
neighbours of $x$ on $C$. Without loss of generality assume that $x^-\in T_1$
and $x^+\in T_3$. Consider any $H$-path $P\subseteq G-X$ such that $x\in
V(\pi(P))$ (so in particular $P\subseteq G_C-e^*$). Since $\pi(P)$ is a
path contained in $H_C-e^*$, the endpoints of $P$ must be in two
different trees. However, it cannot happen that one endpoint of $P$ is in $T_1$
and the other in $T_3$, since then $T_1 \cup T_3 \cup P$ would contain an
$A$-$B$-path, contradicting the fact that $x$ is an $A$-$B$-cut vertex in
$G_C-e^*$. For the same reason there are no two $H$-paths $P_1,
P_2\subseteq G-X$ such that $x\in V(\pi(P_1))\cap V(\pi(P_2))$ and such that
$P_1$ has endpoints in $T_1$ and $T_2$ and $P_2$ has endpoints in $T_2$ and
$T_3$. We conclude that there is some $j\in \{1,3\}$ such that all $H$-paths
$P$ with $x\in V(\pi(P))$ have one endpoint in $T_2$ and the other endpoint in
$T_j$. Without loss of generality, assume $j=1$.
We now claim that by adding the edge $\{x, x^+\}$ to $X$ we get again a $\pi$-preserving set. If we assume otherwise, then there exists a $H$-path
$P$ in $G - (X\cup \{\{x,x^+\}\})$ whose projection contains $\{x, x^+\}$. This
is not possible, as such a path satisfies $x\in V(\pi(P))$ and has one endpoint
lying in $T_3$. Thus $X \cup \{\{x,x^+\}\}$ is $\pi$-preserving. In fact, since the edge
$\{x,x^+\}$ is incident to the degree-three vertex $x$, it is automatically a
valid $\pi$-preserving set. This contradicts the maximality of $X$ and completes the proof
of Lemma \ref{lemma:forest-cut}.

We now present the missing proof of Claim~\ref{claim:obvious}.

\begin{proof}[Proof of Claim \ref{claim:obvious}]
  The second statement clearly follows from the first.

  We start the proof with an observation about the $H$-paths in $G-X$ whose
  endpoints lie in $V(H_C)$. Let $P\subseteq G-X$ be such a path with endpoints
  $a,b\in V(H_C)$. Since $X$ is $\pi$-preserving, we have $\pi(P)\subseteq H-X$.
  Note that we know of at least one path in $H-X$ from $a$ to $b$: the path $Q
  = Q_1Q_2Q_3$, where $Q_1$ is the shortest path in $H_C$ from $a$ to $p(a)$,
  $Q_2$ is the shortest path from $p(a)$ to $p(b)$ on $C$, and $Q_3$ is the
  shortest path from $p(b)$ to $b$ in $H_C$. This path $Q$ is contained in
  $H_C$ and it has length at most $2l+|C|/2$.
  The important observation is that $\pi(P) = Q$. Indeed, if this were not so,
  then $Q\cup \pi(P) \subseteq H-X$ would contain a cycle of length at most
  $2l+|C|/2 + |\pi(P)| \leq 3l+|C|/2<|C|$ (using $|C|>6l$), contradicting the
  minimality of $C$.

  This shows in particular that for every $H$-path $P\subseteq G-X$ with
  endpoints in $V(H_C)$, we have $\pi(P)\subseteq H_C$. It remains to show the
  stronger statement that if additionally $P\subseteq G_C$, then
  $\pi(P)\subseteq H_C-e^*$.

  To obtain a contradiction, assume that $P\subseteq G_C$ is an $H$-path with
  endpoints $a,b\in V(H_C)$ such that $\{x_0,x_n\}\in E(\pi(P))$. Since the
  projection of $P$ has length at most $l$, and by the observation above, we
  can assume without loss of generality that $p(a)\in \{x_0,\dotsc,x_l\}$ and
  $p(b)\in \{x_{n-l},\dotsc,x_n\}$. Now let $c$ be the neighbour of $a$ on $P$.
  The edge $\{a,c\}$ belongs to $G_C$ but not to $H_C$, so there is some $x\in
  D=\{x_l,\dotsc,x_{n-l}\}$ and some $H$-path $P'\in P(x)$ such that
  $\{a,c\}\in E(P')$. Let $d$ be the other endpoint of $P'$ (one endpoint is
  $a$). Since $|C|>6l$, $x\in D$, $x\in V(\pi(P'))$, and $p(a)\in
  \{x_0,\dotsc,x_l\}$, we must have $p(d)\in \{x_l,\dotsc,x_{2l}\}$. The union
  of $P$ and $P'$ contains an $H$-path with endpoints $d$ and $b$. However, the
  projection of this $H$-path has length at least $\min{\{l+1,|C|-3l\}} > l$,
  which is impossible. \end{proof}

\section{Conclusions}

The main contribution of the paper is showing the asymptotically optimal
Erd\H{o}s-P\'osa function for the case of long cycles and growing $k$ and
$\ell$ and thus answering the question asked in \cite{bondy07} and
\cite{fiorini14}. We conclude the paper by mentioning some open problems:

\begin{itemize}
  \item{\textbf{$S$-cycles:}} Kakimura, Kawarabayashi, and
    Marx~\cite{kakimura2011} introduced a different generalization of the
    standard Erd\H{o}s-P\'osa{} theorem. They considered the family of $S$-cycles, i.e., all
    cycles of a graph which intersect a specified set $S$, and proved that such
    a family of cycles has the Erd\H{o}s-P\'osa{} property. Their result was later improved
    by Pontecorvi and Wollan~\cite{pontecorvi2012}, resulting in the following theorem:

    \begin{theorem}
      For any graph and any vertex subset $S$, the graph either contains $k$
      vertex-disjoint $S$-cycles or a vertex set of size $\mathcal{O}(k \log k)$
      that meets all $S$-cycles.
    \end{theorem}

    Since the vertex set $S$ can be the vertex set of the whole graph, this
    result is asymptotically tight. In 2014, Bruhn, Joos, and Schaudt
    \cite{bruhn2014long} combined the family of $S$-cycles with the family of
    long cycles and proved that the family of $S$-cycles of length at least
    $\ell$ has the Erd\H{o}s-P\'osa{} property with $f(k, \ell) = O(\ell k \log k)$. Thus,
    it is natural to ask if Theorem \ref{thm:main} generalizes to $S$-cycles as
    well.

  \item{\textbf{Edge-version:}} A family of graphs $\mathcal{F}$ is said to have the
    \emph{edge-Erd\H{o}s-P\'osa{}} property if there exists a function $f \colon \mathbb{N} \to
    \mathbb{R}$ such that every graph $G$ which does not contain $k$
    edge-disjoint members of $\mathcal{F}$ contains a set of $f(k)$ edges
    which meets all copies of members of $\mathcal{F}$ in $G$. Since the
    pioneering papers by  Erd\H{o}s and P\'osa \cite{erdos62,erdos65} it has
    been known that the family of cycles has the edge-Erd\H{o}s-P\'osa{} property as well.
    Namely, the following is true:
    \begin{theorem*}
      Any graph $G$ contains either $k$ edge-disjoint cycles or a set of $(2 +
      o(1)) k \log k$ edges meeting all its cycles.
    \end{theorem*}

    Pontecorvi and Wollan \cite{pontecorvi2012} generalized this result to the
    case of $S$-cycles by a clever reduction to the standard vertex-version of the
    problem. Already Birmel\'e et al.~\cite{bondy07} asked if the family of long
    cycles has the edge-Erd\H{o}s-P\'osa{} property. Unfortunately, the gadget trick from
    \cite{pontecorvi2012} breaks down in the case of long cycles and thus
    nothing is known in this scenario. It would be interesting to see if
    our approach could be applied for proving that the family of long cycles
    has the edge-Erd\H{o}s-P\'osa{} property.
\end{itemize}

\bibliographystyle{abbrv}

redpajama_set_name: RedPajamaArXiv


text:
Faith in Humanity Restored, Partially
I walked into a Indian/Pakistani restaurant (I still can't say the difference) a few hours ago ago, I asked for a menu card and they didn't understand, none of them spoke any English. As I went in and sat down someone swayed his head about thirty degrees to either side of the vertical axis and said 'Teekay' (I think that's what it was), I have been briefed just enough to say, 'yes, thank you'. Not having a menu, I asked what types of chicken curry they had, the elderly man serving me told a whole string of varieties of which I couldn't recognise or catch any, I heard the word Tandoori and I said okay Tandoori, 'leggu' 'breshtu' came the response, leg I replied, with an air of sophistication. The food got late to come, I enquired from another elderly waiter by gesticulating when the food will arrive, and he said something in Hindi/Urdu which I think was something along the lines of 'on the way'.
The chicken curry came in a plate, with gravy in a bowl and a massive tandoori roti on another plate. I started eating, as one does. I tore the roti in half, not having room to place the other half anywhere I placed it in such a way that it covered the gravy bowl, and about an inch of it may have touched the clean table top.
By this time I had aroused the curiosity of all the waiters (who all were elderly men past their mid to late fifties). They kept looking at me furtively to see who this Indian-looking-non-hindi-speaking English speaking chap was. I occasionally heard pointed whispers.
I felt a bit like Ross from Friends, when all the doctors were looking at the mole on his back.
Some moments later, a third waiter came up to me, removed the roti that was covering my bowl of gravy, took it away and gave me a full fresh roti on a separate plate. A short moment later, yet another waiter arrived and offered me a cup of tea, I told him that I didn't order one, unable to communicate he smiled endearingly and insisted that I take the cup of tea, I realised later that I hadn't been charged.
For reasons unknown to me, they were so nice and generous that I am wondering if I came across as deserving sympathy in some way. Surely they didn't know that I was tired and have a lot of writing work to finish.
I debated if I should leave a tip behind, I felt leaving a tip may come across as being disrespectful since their niceness towards me was most certainly genuine, and not some residual kindness stemming from capitalistic motives. I did leave a tip anyway. On a sub conscious level I was uttering prayers for them unconsciously, that their business should be profitable and that goodness blankets them, I can't really say though, it wasn't on a conscious plane.
Faith in humanity restored, partially.
Forgive the anti-climax.
Tagged as food, india, language, pakistan, personal, restaurant, street, tandoori roti, vertical axis
by Raashid Riza | March 8, 2013 · 12:17 pm
Ed Miliband the Zionist?
Much speculation has been made of Ed Miliband, the man who many (myself included) feel will be the first Jewish Prime Minister of Britain. Guido Falks tweeted an article from The Jewish Chronicle which says that Ed Miliband claims to be a Zionist. Let's go through the exact words –
"I take anti-semitism very seriously. Any kind of de-legitimisation of Israel is something we should call out for what it is and not tolerate it. "I think the boycotts of Israel are totally wrong. We should have no tolerance for boycotts. I would say that to any trade union leaders."
The Haaretz in it's reports quite explicitly points out that when someone asked him if he was a Zionist, Ed replied – "Yes, I consider myself a supporter of Israel." , however Ed was very careful not to say "Yes, I am a Zionist".
Let's be honest here, there is absolutely no way that Ed Miliband can become the next British Prime Minister if he antagonises the right wing pro-Israeli British media, let's be honest about it, no if's and but's. If he takes an openly anti Israeli line the media is going to make sure that he will not be the next British PM and they will not rest until they do. If the British media was to somehow (as if by divine intervention) change their tune and become tacitly pro-Palestinian, then the Zionist lobby in the US will strain every sinew of its special relationship with London to ensure that Miliband does not become PM.
It was quite sad that the Stop The War Coalition with whom I side most of the time tweeted saying 'Labour leader Ed Miliband establishes his pro-Israel credentials like never before & declares he's a Zionist'. This I think is rather misleading, and at least the STWC should have been more considerate of whom they want to be friendly with.
About Ed Miliband, let's establish a few home truths.
Ed Miliband was raised an atheist by his parents, his father was the radical Marxist intellectual Ralph Miliband and his mother Marion Kozac is a signatory for the founding statements of 'Jews for Justice for Palestinians'.
Ed Miliband was elected leader largely due to the trade unions. Britains largest trade unions, UNITE and UNISON have both passed a motion to boycott goods from Israeli settlements.
In his very first speech as Labour leader, Miliband said this.
When Mossad used forged British Passports to carry out a failed assassination bid against a Hamas official in Dubai when his brother David Miliband was the foreign Secretary, there was very significant diplomatic friction between Israel and the UK.
Ed Miliband has been very openly attending events and supporting Labour Friends of Palestine, something neither of his New Labour predecessors did.
Compare and contrast Ed Miliband with Tony Blair and to a lesser extent Gordon Brown vis a vis the Israeli question and you'll see that Miliband actually comes out uncontaminated by any Israeli links. Also, let's not forget, contrary to what anyone might say, it was Miliband who took on the highly influential Israeli poodle that is Rupert Murdoch.
I don't see how anything Miliband said yesterday can be spelled out as doom saying for the pro Palestinian activists. I think it is wise and indeed incumbent upon him to woo the Israeli lobby if there is any chance of him becoming PM.
It is only fair to him that he is judged on his record as PM, until then he deserves the respite.
Filed under 2013, england, politics, Uncategorized
Tagged as Israel, middle-east, Miliband, Palestine, politics, prime minister of britain, uk, Westminister, Zionist

redpajama_set_name: RedPajamaCommonCrawl


text:
Fórum > Meteorologia e Climatologia > Climatologia >
Erupções vulcânicas e os seus efeitos no clima
Tópico em 'Climatologia' iniciado por Vince 27 Abr 2009 às 11:14.
27 Abr 2009 às 11:14#1
É habitual falar-se no seguimento dos Vulcões dos efeitos dos mesmos no clima de cada vez que temos uma erupção. Resolvi criar este tópico para reunir alguns artigos e a discussão sobre os mesmos. O impacto dos vulcões pode ser significativo em determinadas circunstâncias ou pode não o ser. Por vezes arrefecem tremendamente a Terra, noutras condições podem até aquecer.
A leitura da serie de artigos que vou colocar vai ajudar a compreender a complexidade do assunto e também ajuda a perceber o importante papel dos vulcões nos muito criticados modelos climáticos dado que as erupções significativas são boas para testar e validar de forma prática muitos factores dos próprios modelos.
#1 Vince, 27 Abr 2009 às 11:14
Comecemos por um artigo sobre a recente erupção do Redoubt e dos porquês desta erupção provavelmente ter até à data um efeito menor no clima
Redoubt volcano unlikely to have a major climate impact
Alaska's Redoubt Volcano continues to erupt, with the latest blast coming just after midnight Eastern time (7:41pm AKDT). The latest eruption threw ash 50,000 feet into the air, but the ash has settled to the ground and the ashfall advisory for cities to the north and northwest of Anchorage such as Talkeetna has expired. Redoubt is located about 100 miles southwest of Alaska's most populous city, Anchorage. The prevailing southerly winds deposited a swath of ash about 200 miles long to the north of the volcano (Figure 1). Redoubt last erupted between December 1989 - April 1990, and its ash clouds presented a major hazard to aviation. On December 16, 1989, Redoubt's eruption spewed ash into the air to a height of 14,000 m (45,000 ft) catching KLM Royal Dutch Airlines flight 867, a Boeing 747 aircraft, in the plume. All four engines stalled and the aircraft plummeted 13,000 feet before the pilot was able to restart the engines and land safely in Anchorage. The total costs to the aviation industry from the 1989 - 1990 eruption were about $100 million. Eighty percent of these costs were due to damaged equipment. For more information on the Redoubt eruption, check out the Alaska Volcano Observatory home page.
Figure 1. Ash on the snow to the north of Alaska's Mt. Redoubt crater in this true color image from NASA's Terra satellite. Image taken 21:49 GMT March 23, 2009. Image credit: Johnathan Dehn, Geographic Information Network of Alaska..
Redoubt's effect on the climate should be minimal
Many historic volcanic eruptions have had a major cooling impact on Earth's climate. However, Redoubt is very unlikely to be one of them. To see why this is, let's examine recent volcanic eruptions that have had a significant cooling effect on the climate. In the past 200 years, Mt. Pinatubo in the Philippines (June 1991), El Chichon (Mexico, 1982), Mt. Agung (Indonesia, 1963), Santa Maria (Guatemala, 1902) Krakatoa (Indonesia, 1883), and Tambora (1815) all created noticeable cooling. As one can see from a plot of the solar radiation reaching Mauna Loa in Hawaii (Figure 2), the Mt. Pinatubo and El Chichon eruptions caused a greater than 10% drop in sunlight reaching the surface. The eruption of Tambora in 1815 had an even greater impact, triggering the famed Year Without a Summer in 1816. Killing frosts and snow storms in May and June 1816 in Eastern Canada and New England caused widespread crop failures, and lake and river ice were observed as far south as Pennsylvania in July and August. Volcanic eruptions cause this kind of climate cooling by throwing large amounts of sulfur dioxide gas into the stratosphere. This gas reacts with water to form sulphuric acid droplets (aerosol particles), which are highly reflective, and reduce the amount of incoming sunlight.
Figure 2. Reduced solar radiation due to volcanic aerosols as measured at Mauna Loa Observatory, Hawaii. Image credit: NOAA/ESRL.
You'll notice from the list of eruptions above that all of these climate-cooling events were from volcanoes in the tropics. Above the tropics, the stratosphere's circulation features rising air, which pulls the sulfur-containing volcanic aerosols high into the stratosphere. Upper-level winds in the stratosphere tend to flow from the Equator to the poles, so sulfur aerosols from equatorial eruptions get spread out over both hemispheres. These aerosol particles take a year or two to settle back down to earth, since there is no rain in the stratosphere to help remove them. However, if a major volcanic eruption occurs in the mid-latitudes or polar regions, the circulation of the stratosphere in those regions generally features pole-ward-flowing, sinking air, and the volcanic aerosol particles are not able to penetrate high in the stratosphere or get spread out around the entire globe. Redoubt is located near 59° north latitude, far from the tropics, and thus is unlikely to be able to inject significant amounts of sulfur aerosols into the stratosphere. Furthermore, the previous 1989 - 1990 eruption of Redoubt (Figure 3) put only about 1/100 of the amount of sulfur into the air that the 1991 eruption of Mt. Pinatubo did, according to the TOMS Volcanic Emissions Group. We can expect the current eruption of Redoubt to be similar in sulfur emissions to the 1989 - 1990 eruption, and have an insignificant impact on global climate.
Figure 3. Amount of sulfur gases put into the air by recent volcanic eruptions. Note that the 1989 eruption of Redoubt put only 1/100 the amount of sulfur dioxide (SO2) into the air that the 1991 eruption of Mt. Pinatubo did. Image credit: TOMS Volcanic Emissions Group.
http://www.wunderground.com/blog/JeffMasters/comment.html?entrynum=1203&tstamp=#commenttop
Agora um artigo mais abrangente com interessantes dados do passado, com muitas ligações externas e com um gráfico impressionante da simulação da erupção do Toba há 74,000 anos, com as temperaturas um ano depois a manterem-se em Terra cerca de 12 a 16ºC mais baixas a nível global.
Volcanic Winter
"The sun was dark and its darkness lasted for eighteen months; each day it shone for about four hours; and still this light was only a feeble shadow; the fruits did not ripen and the wine tasted like sour grapes."
As this Michael the Syrian quote regarding the weather of 536 A.D. demonstrates, a climate catastrophe that blots out the sun can really spoil your day. Procopius of Caesarea remarked: "During this year [536 A.D.] a most dread portent took place. For the sun gave forth its light without brightness. and it seemed exceedingly like the sun in eclipse, for the beams it shed were not clear." Many documents from 535 - 536 A.D.--the time of King Arthur in Britain--speak of the terrible "dry fog" or cloud of dust that obscured the sun, causing widespread crop failures in Europe, and summer frosts, drought, and famine in China. Tree ring studies in Europe confirm several years of very poor growth around that time, and ice cores from Greenland and Antarctica show highly elevated levels of atmospheric sulfuric acid dust existed.
Though some scientists believe the climate calamity of 535-536 A.D. was due to a comet or asteroid hitting the Earth, it is widely thought that the event was probably caused by the most massive volcanic eruption of the past 1500 years. This eruption threw so much sulfur dioxide (SO2) gas into the stratosphere that a "Volcanic Winter" resulted. Sulfur dioxide reacts with water to form sulfuric acid droplets (aerosol particles), which are highly reflective and reduce the amount of incoming sunlight. The potential eruption that led to the 535 - 536 A.D. climate calamity would have likely been a magnitude 7 event on the Volcanic Explosivity Index (VEI)--a "super colossal" eruption that one can expect to occur only once every 1000 years. The Volcanic Explosivity Index is a logarithmic scale like the Richter scale used to rate earthquakes, so a magnitude 7 eruption would eject ten times more material than the two largest eruptions of the past century--the magnitude 6 eruptions of Mt. Pinatubo in the Philippines (1991) and Novarupta in Alaska (1912).
Figure 1. An 18 km-high volcanic plume from one of a series of explosive eruptions of Mount Pinatubo beginning on 12 June 1991, viewed from Clark Air Base (about 20 km east of the volcano). Three days later, the most powerful eruption produced a plume that rose nearly 40 km, penetrating well into the stratosphere. Pinatubo's sulfur emissions cooled the Earth by about 1°F (0.5°C) for 1 - 2 years. (Photograph by David H. Harlow, USGS.)
Super-colossal eruptions
There has been only one other magnitude 7 "super-colossal" eruption in the past 1500 years--the massive eruption of the Indonesian volcano Tambora in 1815. The sulfur pumped by this eruption into the stratosphere dimmed sunlight so extensively that global temperatures fell by about 2°F (1°C) for 1 - 2 years afterward. This triggered the famed Year Without a Summer in 1816. Killing frosts and snow storms in May and June 1816 in Eastern Canada and New England caused widespread crop failures, and lake and river ice were observed as far south as Pennsylvania in July and August. The Tambora eruption was about 40% smaller than the 535 - 536 A.D. event, as measured by the number of sulfur aerosol particles deposited in Greenland ice cores.
In an article published in 2008 in the American Geophysical Union journal EOS, Dr. Ken Verosub of the University of California, Davis Department of Geology estimated that future eruptions capable of causing "Volcanic Winter" effects severe enough to depress global temperatures by 2°F (1°C) and trigger widespread crop failures for 1 - 2 years afterwards should occur about once every 200 - 300 years. Even a magnitude 6 eruption, such as the 1600 eruption of the Peruvian volcano Huaynaputina, can cause climatic change capable of killing millions of people. The Huaynaputina eruption is blamed for the Russian famine of 1601-1603, which killed over half a million people and led to the overthrow of Tsar Boris Godunov. Thankfully, the climatic impacts of all of these historic magnitude 6 and 7 eruptions have been relatively short-lived. After about two years, the sulfuric acid aerosol particles have settled out of the stratosphere, returning the climate to its former state.
Mega-colossal eruptions
Even more extreme eruptions have occurred in Earth's past--eruptions ten times more powerful than the Tambora eruption, earning a ranking of 8 out of 8 on the Volcanic Explosivity Index (VEI). These "mega-colossal" eruptions occur only about once every 10,000 years, but have much longer-lasting climatic effects and thus are a more significant threat to human civilization. According to the Toba Catastrophe Theory, a mega-colossal eruption at Toba Caldera, Sumatra, about 74,000 years ago, was 3500 times greater than the Tambora eruption. According to model simulations, an eruption this large can pump so much sulfur dioxide gas into the stratosphere that the atmosphere does not have the capacity to oxidize all the SO2 to sulfuric acid aerosol. The atmosphere oxidizes as much SO2 as it can, leaving a huge reservoir of SO2 in the stratosphere. This SO2 gradually reacts to form sulfuric acid as the OH radicals needed for this reaction are gradually produced. The result is a much longer-lasting climate effect than the 1 - 2 years that the magnitude 6 and 7 events of 535, 1600, 1815, and 1991 lasted. A magnitude 8 eruption like the Toba event can cool the globe for 6 - 10 years (Figure 3), which may be long enough to trigger an ice age--if the climate is already on the verge of tipping into an ice age. Rampino and Self (1992) argued that the sulfur aerosol veil from Toba was thick and long-lasting enough to cool the globe by 3 - 5°C (5 - 9°F), pushing the climate--which was already cooling and perhaps headed towards an ice age--into a full-scale ice age. They suggested that the response of Canada to the volcano played a particularly important role, with their model predicting a 12°C (22°F) reduction in summer temperatures in Canada. This would have favored the growth of the Laurentide ice sheet, increasing the reflectivity (albedo) of the Earth, reflecting more sunlight and reducing temperatures further. The controversial Toba Catastrophe Theory asserts that the resulting sudden climate change reduced the Earth's population of humans to 1,000 - 10,000 breeding pairs. More recent research has shed considerable doubt on the idea that the Toba eruption pushed the climate into an ice age, though. Oppenheimer (2002) found evidence supporting only a 2°F (1.1°C) cooling of the globe, for the 1000 years after the Toba eruption. Zielinski et al. (1996) argued that the Toba eruption did not trigger a major ice age--the eruption merely pushed the globe into a cool period that lasted 200 years. Interestingly, a previous super-eruption of Toba, 788,000 years ago, coincided with a transition from an ice age to a warm period.
Figure 2. The 100x30 square kilometer Toba Caldera is situated in north-central Sumatra around 200 km north of the Equator. It is comprised of four overlapping calderas aligned with the Sumatran volcanic chain. Repeated volcanic cataclysms culminated in the stupendous expulsion of the Younger Toba Tuff around 74,000 years ago. The lake area is 100 square kilometers. Samosir Island formed as a result of subsequent uplift above the evacuated magma reservoir. Such resurgent domes are typically seen as the concluding phase of a large eruption. Landsat Enhanced Thematic Mapper Plus (ETM+) browse images for path/row 128/58 (6 September 1999) and 129/58 (21 January 2001) from http://landsat7.usgs.gov/. Copyright USGS. Image source: Oppenheimer, C., 2002, "Limited global change due to the largest known Quaternary eruption, Toba 74 kyr BP?"Quaternary Science Reviews, 21, Issues 14-15, August 2002, Pages 1593-1609.
Figure 3. Total mass of sulfur dioxide and sulfate aerosol in the stratosphere (heavy solid and dotted lines, respectively) modeled for a 6 petagram stratospheric injection of SO2. Observed SO2 and aerosol mass for the 1991 Pinatubo eruption are shown for comparison. The much larger amount of SO2 in the Toba simulation soaks up all available oxidants in the stratosphere leading to a much longer lifetime of SO2 and, in turn, prolonging the manufacture of sulfate aerosol. Data from Read et al. (1993) and Bekki et al. (1996). Image source: Oppenheimer, C., 2002, "Limited global change due to the largest known Quaternary eruption, Toba 74 kyr BP?"Quaternary Science Reviews, 21, Issues 14-15, August 2002, Pages 1593-1609.
When can we expect the next mega-colossal eruption?
Given the observed frequency of one mega-colossal magnitude 8 volcanic eruption every 1.4 million years, the odds of another hitting in the next 100 years is about .014%, according to Mason et al., 2004. This works out to a 1% chance over the next 7200 years. Rampino (2002) puts the average frequency of such eruptions at once every 50,000 years--about double the frequency with which 1-km diameter comets or asteroids capable of causing a similar climatic effect hit the Earth. A likely location for the next mega-colossal eruption would be at the Yellowstone Caldera in Wyoming, which has had magnitude 7 or 8 eruptions as often as every 650,000 years. The last mega-colossal eruption there was about 640,000 years ago. But don't worry, the seismic activity under Yellowstone Lake earlier this year has died down, and the uplift of the ground over the Yellowstone caldera that was as large as 7 cm/yr (2.7 inches/yr) between 2004 - 2006 has now fallen to 4 cm/yr, according to the Yellowstone Volcano Observatory. The USGS states that "the Yellowstone volcanic system shows no signs that it is headed toward such an eruption. The probability of a large caldera-forming eruption within the next few thousand years is exceedingly low".
What would happen if a magnitude 8 mega-colossal eruption were to occur today?
If a mega-colossal eruption were to occur today, it would probably not be able to push Earth into an ice age, according to a modeling study done by Jones et al. (2005). They found that an eruption like Toba would cool the Earth by about 17°F (9.4°C) after the first year (Figure 3), and the temperature would gradually recover to 3°F (1.8°C) below normal ten years after the eruption. They found that the eruption would reduce rainfall by 50% globally for the first two years, and up to 90% over the Amazon, Southeast Asia, and central Africa. This would obviously be very bad for human civilization, with the cold and lack of sunshine causing widespread crop failures and starvation of millions of people. Furthermore, the eruption would lead to a partial loss of Earth's protective ozone layer, allowing highly damaging levels of ultraviolet light to penetrate to the surface.
Not even a mega-colossal eruption of this magnitude would stop global warming, though. The level of greenhouse gases in the atmosphere would not be affected by the volcanic eruption, and warming would resume where it left off once the stratospheric dust settled out in a decade. With civilization crippled by the disaster, greenhouse gas emissions would be substantially reduced, though (small solace!) If we really want to say goodbye to civilization, a repeat of the only magnitude 9 eruption in recorded history should do the trick--the magnitude 9.2 La Garita, Colorado blast of 27.8 million years ago (Mason et al., 2004).
Figure 4. Annual near-surface temperature anomalies for the year following a mega-colossal volcanic eruption like the Toba eruption of 74,000 years ago, if it were to occur today. Most land areas cool by 22°F (12°C) compared to average. Some areas, like Africa, cool by 29°F (16°C). Image credit: Jones, G.S., et al., 2005, "An AOGCM simulation of the climate response to a volcanic super-eruption", Climate Dynamics, 25, Numbers 7-8, pp 725-738, December, 2005.
What would happen if a magnitude 7 super-colossal eruption were to occur today?
An eruption today like the magnitude 7 events of 535 A.D. or 1815 would cause cause wide-spread crop failures for 1 - 2 years after the eruption. With food supplies in the world already stretched thin by rising population, decreased water availability, and conversion of cropland to grow biofuels, a major volcanic eruption would probably create widespread famine, threatening the lives of millions of people. Wars over scarce resources might result. However, society's vulnerability to major volcanic eruptions is less than it was, since the globe has warmed significantly in the past 200 years. The famines from the eruptions of 1600 and 1815 both occurred during the Little Ice Age, when global temperatures were about 1.4°F (0.8°C) cooler than today. Crop failures would not be as wide-spread with today's global temperatures, if a suer-colossal eruption were to occur. Fifty years from now, when global temperatures are expected to be at least 1°C warmer, a magnitude 7 eruption should only be able to cool the climate down to year 2009 levels.
Volcanoes also warm the climate
While volcanoes cool the climate on time scales of 1 - 2 years, they act to warm the climate over longer time scales, since they are an important source of natural CO2 to the atmosphere. Volcanoes add 0.1 - 0.3 gigatons (Gt) of carbon to the atmosphere each year, which is about 1 - 3% of what human carbon emissions to the atmosphere were in 2007, according to the Global Carbon Project. In fact, volcanoes are largely responsible for the natural CO2 in the atmosphere, and helped make life possible on Earth. Why, then, haven't CO2 levels continuously risen over geologic time, turning Earth into a steamy hothouse? In fact, CO2 levels have fallen considerably since the time of the dinosaurs--how can this be? Well, volcano-emitted CO2 is removed from the atmosphere by chemical weathering. This occurs when rain and snow fall on rocks containing silicates. The moisture and silicates react with CO2, pulling it out of the air. The carbon removed from the air is then washed into the sea, where it ends up in ocean sediments that gradually harden into rock. Rates of chemical weathering on Earth have accelerated since the time of the dinosaurs, largely due to the recent uplift of the Himalaya Mountains and Tibetan Plateau. These highlands undergo a tremendous amount of weathering, thanks to their lofty heights and the rains of the Asian Monsoon that they capture. Unfortunately, chemical weathering cannot help us with our current high levels of greenhouse gases, since chemical weathering takes thousands of years to remove significant amounts of CO2 from the atmosphere. It takes about 100,000 years for silicate weathering to remove 63% of the CO2 in the atmosphere. Thus, climate models predict that chemical weathering will solve our greenhouse gas problem in about 100,000 - 200,000 years.
PBS TV special on the 535-536 A.D. disaster.
Newspaper articles on the 535-536 A.D. disaster.
Volcanic winter article from wikipedia.
Realclimate.org has a nice article that goes into the volcano-climate connection in greater detail.
Bekki, S., J.A. Pyle, W. Zhong, R. Toumi, J.D. Haigh and D.M. Pyle, 1996, "The role of microphysical and chemical processes in prolonging the climate forcing of the Toba eruption", Geophysical Research Letters 23 (1996), pp. 2669-2672.
Jones, G.S., et al., 2005, "An AOGCM simulation of the climate response to a volcanic super-eruption", Climate Dynamics, 25, Numbers 7-8, pp 725-738, December, 2005.
Rampino, M.R., and S. Self, 1993, "Climate-volcanism feedback and the Toba eruption of 74,000 years ago", Quaternary Research 40 (1993), pp. 269-280.
Mason, B.G., D.M. Pyle, and C. Oppenheimer, 2004, "The size and frequency of the largest observed explosive eruptions on Earth", Bulletin of Volcanology" 66, Number 8, December 2004, pp 735-748.
Oppenheimer, C., 2002, "Limited global change due to the largest known Quaternary eruption, Toba 74 kyr BP?"Quaternary Science Reviews, 21, Issues 14-15, August 2002, Pages 1593-1609.
Rampino, M.R., 2002, "Supereruptions as a Threat to Civilizations on Earth-like Planets", Icarus, 156, Issue 2, April 2002, Pages 562-569.
Read, W.G., L. Froidevaux and J.W. Waters, 1993, "Microwave Limb Sounder measurements of stratospheric SO2 from the Mt. Pinatubo eruption", Geophysical Research Letters 20 (1993), pp. 1299-1302.
Verosub, K.L., and J. Lippman, 2008, "Global Impacts of the 1600 Eruption of Peru's Huaynaputina Volcano", EOS 89, 15, 8 April 2008, pp 141-142.
Zielinski, G.A. et al., 1996, "Potential Atmospheric Impact of the Toba Mega-Eruption 71,000 Years Ago", Geophysical Research Letters, 23, 8, pp. 837-840, 1996.
http://www.wunderground.com/blog/JeffMasters/comment.html?entrynum=1213#commenttop
Agora um exemplo de uma grande erupção não tropical ocorrida em 1912, a do Vulcão Novarupta no Alasca a sul do circulo Árctico, a maior erupção do século XX equivalente à do Krakatoa de 1883, mas em que os efeitos no clima foram diferentes de outras erupções como as tropicais, afectando por exemplo as monções na Índia trazendo tempo quente e seco aquela região.
Huge volcano blast tweaked world weather
In June 1912, Novarupta—one of a chain of volcanoes on the Alaska Peninsula—erupted in what turned out to be the largest blast of the twentieth century. It was so powerful that it drained magma from under another volcano, Mount Katmai, six miles east, causing the summit of Katmai to collapse to form a caldera half a mile deep. Novarupta also expelled three cubic miles of magma and ash into the air, which fell to cover an area of 3,000 square miles more than a foot deep.
Despite the fact that the eruption was comparable to that of the far more famous eruption of Krakatau in Indonesia in 1883 and so near the continental United States, it was hardly known at the time because the area was so remote from English-speaking people.
Almost a hundred years later, researchers are paying attention. Novarupta is near the Arctic Circle and its impact on climate appears to be quite different from that of "ordinary" tropical volcanoes, according to recent research by climatologists using a NASA computer model.
When a volcano anywhere erupts, it does more than spew clouds of ash, which can shadow a region from sunlight and cool it for a few days. It also blows sulfur dioxide—a gas irritating to the lungs and smelling like rotten eggs. If the eruption is strongly vertical, it shoots that sulfur dioxide high into the stratosphere more than 10 miles above Earth.
Up in the stratosphere, sulfur dioxide reacts with water vapor to form sulfate aerosols. Because these aerosols float above the altitude of rain, they don't get washed out. They linger, reflecting sunlight and cooling Earth's surface.
This can create a kind of nuclear winter (a.k.a. "volcanic winter") for a year or more after an eruption. In April 1815, for instance, the Tambora volcano in Indonesia erupted. The following year, 1816, was called "the year without a summer," with snow falling across the United States in July. Even the smaller June 1991 eruption of Pinatubo in the Philippines cooled the average temperature of the northern hemisphere summer of 1992 to well below average.
But both those volcanoes as well as Krakatau were in the tropics.
Novarupta is just south of the Arctic Circle.
Using a NASA computer model at the the Goddard Institute for Space Studies (GISS), Prof. Alan Robock of Rutgers University and colleagues found that Novarupta's effects on the world's climate would have been different. (Their research was funded by the National Science Foundation.)
Robock explains: "The stratosphere's average circulation is from the equator to the poles, so aerosols from tropical volcanoes tend to spread across all latitudes both north and south of the Equator." Aerosols would quickly circulate to all parts of the globe.
But the NASA GISS climate model showed that aerosols from an arctic eruption such as Novarupta tend to stay north of 30ºN—that is, no further south than the continental United States or Europe. Indeed, they would mix with the rest of Earth's atmosphere only very slowly.
Fig. The inner workings of "volcanic winter," from Robock, Alan, 2000: Volcanic eruptions and climate. Rev. Geophys., 38, 191-219. Copyright 2000 AGU.
This bottling up of Novarupta's aerosols in the north would make itself felt, strangely enough, in India. According to the computer model, the Novarupta blast would have weakened India's summer monsoon, producing "an abnormally warm and dry summer over northern India," says Robock.
Why India? Cooling of the northern hemisphere by Novarupta would set in motion a chain of events involving land and sea surface temperatures, the flow of air over the Himalayan mountains and, finally, clouds and rain over India. It's devilishly complex, which is why supercomputers are needed to do the calculations.
To check the results, Robock and colleagues are examining weather and river flow data from Asia, India, and Africa in 1913, the year after Novarupta. They are also investigating the consequences of other high-latitude eruptions in the last few centuries.
Do Indians need to keep an eye on Arctic volcanoes? The GISS computer says so. Stay tuned to Science@NASA for updates.
http://science.nasa.gov/headlines/y2006/03oct_novarupta.htm
Agora um link para estudo muito completo de 30 páginas sobre esta temática:
VOLCANIC ERUPTIONS AND CLIMATE
Alan Robock
Department of Environmental Sciences
Abstract. Volcanic eruptions are an important natural
cause of climate change on many timescales. A new
capability to predict the climatic response to a large
tropical eruption for the succeeding 2 years will prove
valuable to society. In addition, to detect and attribute
anthropogenic influences on climate, including effects of
greenhouse gases, aerosols, and ozone-depleting chemicals,
it is crucial to quantify the natural fluctuations so
as to separate them from anthropogenic fluctuations in
the climate record. Studying the responses of climate to
volcanic eruptions also helps us to better understand
important radiative and dynamical processes that respond
in the climate system to both natural and anthropogenic
forcings. Furthermore, modeling the effects of
volcanic eruptions helps us to improve climate models
that are needed to study anthropogenic effects. Large
volcanic eruptions inject sulfur gases into the stratosphere,
which convert to sulfate aerosols with an e-folding
residence time of about 1 year. Large ash particles
fall out much quicker. The radiative and chemical effects
of this aerosol cloud produce responses in the climate
system. By scattering some solar radiation back to space,
the aerosols cool the surface, but by absorbing both solar
and terrestrial radiation, the aerosol layer heats the
stratosphere. For a tropical eruption this heating is
larger in the tropics than in the high latitudes, producing
an enhanced pole-to-equator temperature gradient, especially
in winter. In the Northern Hemisphere winter
this enhanced gradient produces a stronger polar vortex,
and this stronger jet stream produces a characteristic
stationary wave pattern of tropospheric circulation, resulting
in winter warming of Northern Hemisphere continents.
This indirect advective effect on temperature is
stronger than the radiative cooling effect that dominates
at lower latitudes and in the summer. The volcanic
aerosols also serve as surfaces for heterogeneous chemical
reactions that destroy stratospheric ozone, which
lowers ultraviolet absorption and reduces the radiative
heating in the lower stratosphere, but the net effect is
still heating. Because this chemical effect depends on the
presence of anthropogenic chlorine, it has only become
important in recent decades. For a few days after an
eruption the amplitude of the diurnal cycle of surface air
temperature is reduced under the cloud. On a much
longer timescale, volcanic effects played a large role in
interdecadal climate change of the Little Ice Age. There
is no perfect index of past volcanism, but more ice cores
from Greenland and Antarctica will improve the record.
There is no evidence that volcanic eruptions produce El
Nin˜o events, but the climatic effects of El Nin˜o and
volcanic eruptions must be separated to understand the
climatic response to each.
continua em: (PDF)
http://climate.envsci.rutgers.edu/pdf/ROG2000.pdf
Para finalizar por agora, um estudo português e espanhol recente (Trigo et al. "Iberia in 1816, the year without a summer") sobre o "Ano sem Verão" na Península Ibérica devido à erupção do Tambora na Indonésia em 1815.
Int. J. Climatol. (2008)
Iberia in 1816, the year without a summer
Ricardo M. Trigo, José M. Vaquero, Maria-João Alcoforado, Mariano Barriendos,
João Taborda, Ricardo García-Herrera and Juerg Luterbacherh
ABSTRACT: The year 1816 was characterized by unusual weather conditions, in particular, by a cold and wet summer
season ('year without a summer') on both the European and North American continents. The eruption of Tambora, an active
stratavolcano, on the Island of Sumbaya (Indonesia) in April 1815 has been identified as the main driving force for the strong
1816 temperature anomaly. This climate anomaly has been relatively well studied in central Europe, France, Scandinavia
and the United Kingdom. The unusual unsettled weather and climate at mid-latitudes in 1816 and 1817 had major socioeconomic
impacts, particularly in terms of a poor yield of agricultural production, malnutrition and consequentially an
increased potential for diseases and epidemics. The Iberian Peninsula was also affected by the intense climate anomalies
during those years. Documentary sources describe the impact that the cold and wet summer of 1816 had on agriculture,
namely the bad quality of fruits, delayed ripening of vineyards and cereals.
It is within this context that we stress the relevance of recently recovered meteorological observed data, from 1816
onwards, for stations located in Portugal (Lisbon) and also for a longer period for the Spanish stations of Madrid, Barcelona
and San Fernando-Cadiz. We have compared observed (station-based) and large-scale reconstructed seasonal temperature
anomalies computed for the winter and summer seasons after the eruption (1816–1818). There is qualitative agreement
between the two independent data sets, though some stations partly indicate stronger departures from the long-term averages
for single years compared to neighbouring grid points. In particular, all available stations reveal a cold summer of 1816,
mainly in July and August. In comparison to the 1871–1900 reference period, those two months were 2–3 °C cooler, close
to what has been reported for central Europe. We also discuss the regional climate anomalies for those years (1816–1818)
using independently reconstructed atmospheric circulation fields.
http://www.cgul.ul.pt/Ricardo/pdf/Trigo_etal_IJC_2008.pdf
Forecaster @ https://bestweather.pt/
TROVOADA!!!!
Quem quiser entrar em contacto é só enviar mail para:
geral.bestweather@gmail.com
Sigam o nosso trabalho em:
https://twitter.com/bestweather_pt
https://www.facebook.com/bestweather.pt/
https://www.instagram.com/bestweatherpt/
#7 stormy, 27 Abr 2009 às 14:50


text:
Aunty Kau'I, a fixture at Disney's Polynesian resort, has died
By Dewayne Bevil
Kau'I Brandt, a.ka. Aunty Kau'I, who made leis and taught the hula to thousands of Disney World guests, laughs outside the Polynesian resort in 2014. (Jacob Langston / Orlando Sentinel)
A longtime Walt Disney World worker who greeted guests at Disney's Polynesian Village Resort with handmade leis and sometimes gave hula lessons has died. Kau'I Brandt — known to many people as Aunty Kau'I — was 87.
Brandt, born in 1932 Hawaii, began working at Disney World as part of the opening-day staff in 1971. It was supposed to be a three-month luau gig in Florida after working for a summer at Disneyland. She ended up working at the Polynesian for decades.
"We are all deeply saddened by the passing of Auntie Kau'i, a longtime cast member and Hawaiian icon who brought happiness to millions throughout the years as she took such joy in immersing guests in Polynesian culture," Josh D'Amaro, president of Walt Disney World, said in a statement Friday.
Eventually, Brandt's job title at the Poly became "cultural ambassador." She met incoming guests with fresh-flower leis and grass skirts, entertaining the youngest guests.
"If the kids are happy, the parents are happy," she told the Sentinel in 2009.
She was born during a lightning storm. Her mother named her Kauihealani — or "thundering voice of heaven." A key event in her young life was the morning of Dec. 7, 1941, while sitting on her mother's roof in a town near Pearl Harbor, she told the Sentinel in 2014.
"My mom told me, 'It's war. Get off the roof.' I said, 'What's war?' We didn't know what war was. But, we learned. It was a tough time," she said.
Years later, after learning to hula, she was recruited to be in a show at Disneyland. She said she turned it down multiple times.
"I've always heard once you leave Hawaii, you never go back," she said. "And I guess it's true because we left Hawaii for the summer of 1971, came up here to Florida only to help them open up the Polynesian Resort, and here I am."
Email me at dbevil@orlandosentinel.com. Want more theme park news? Subscribe to the Theme Park Rangers newsletter at orlandosentinel.com/newsletters or the Theme Park Rangers podcast at orlandosentinel.com/travel/attractions/theme-park-rangers-podcast.


September 2018 - Klubfunder - Helping clubs raise funds.
The Air Ambulance NI has launched a membership club for local supporters to join together as a community supporting this great service for the residents in Northern Ireland. Klubfunder helps clubs raise funds and how we do this for the air ambulance is by providing them with a membership payment package on our platform for FREE!


text:
About the Chatham Voice
Send Us Your News/Sports
Canada and World News
Bruce Uncorked
E-Voice
Voice Homes
Laser tag comes to Chatham
Nov 6 • Business, Feature Story • No Comments on Laser tag comes to Chatham
FlashPoint Laser Tag offers people of all ages another recreational option in Chatham. It recently opened on Queen Street.
For residents of all ages gunning for some fun, a new laser tag facility has recently opened in Chatham.
FlashPoint, situated on Queen Street above MicroAge, is now open to the public.
Owner Jay Denorer, a local OPP officer, saw a need in the community.
"I've been thinking about something like this for about three years now," he said. "I was watching social media and saw how people were complaining there is nothing for families to do in the area. This is just something different."
It's also something for which he had to take his own kids out of town to enjoy in the past.
"I drove my kids to Windsor to play down there. The cost was becoming prohibitive," he said. "I thought, 'Why not bring something to town?'"
Laser tag involves participants donning sensors that pick up when a beam from another participants' gun is "fired" at them. After a certain number of hits, that player is eliminated.
Unlike paintball, it's a painless way to play a live first-person shooter (FPS).
And it gets the kids up and moving, unlike an FPS video game where they plant themselves on the couch and give their thumbs a workout on their game controller.
"The biggest takeaway from this is exercise. This is getting them out of the house and getting them moving around. The kids are playing games like Fortnite online anyway," he said. "It's also a great family event."
The grand opening took place Oct. 25 and Denorer said it was well received.
"People had a blast playing around. And the weekend was very busy. We keep having more and more people show up," he said.
Denorer said a minor hockey team tested FlashPoint in several ways, as they arrived with 26 people, ready for some fun.
The owner said he discovered that the businesses approached its maximum.
"The hockey team really tested our equipment, and we now know the maximum number of people we can go with," he said, adding the number is 28.
That's based on the number of laser assault rifles, shotguns, pistols and even knives FlashPoint has on hand.
FlashPoint operates in 4,200 square-feet of space, so even with a full crew in mock combat, there is plenty of room for everyone.
"It looks a lot bigger when you turn the lights out," he said, adding it's not pitch black either. "We have one overhead light and six black lights on the side. You are still able to see, but it's a low-light situation – almost like being outside at night."
Denorer said each participant has a headband with sensors, and a weapon, which also has damage sensors.
"The guns have sensors. You will do weapon damage. If you shoot the gun long enough, you can eventually eliminate the player," he said.
Players know they've been "hit" when their guns or headbands vibrate. Take enough hits and you are temporarily eliminated, as you have to leave the floor to "respawn," Denorer said.
Denorer said parents don't have to worry about any potential optical damage from someone being "shot" in the face by the guns.
"With these lasers, there is no risk whatsoever to the eyes. It's not like a laser pointer where you can actually do damage," he said. "These are very low power and we have acute sensors."
FlashPoint offers a variety of game options, and these are continually expanding, as Denorer said staff are testing out new options every week.
There are death matches, capture the flag, and even zombie apocalypse.
"Every week, we introduce a new one," Denorer said. "It's to give us the experience of using the equipment and seeing its limitations."
You can book birthday parties for the kids, or corporate bonding experiences for businesses.
For more information, visit http://flashpointlasertag.ca/
Chatham-Kentflashpointlaser tag
About the Author: Bruce Corcoran
Bruce Corcoran is a veteran writer, editor and broadcaster, having spent more than two decades in the media industry. His news articles and opinion pieces have appeared in various Sun Media publications, including The Toronto Sun, London Free Press and Chatham Daily News; as well as The Toronto Star; National Post; Metroland publications; and The Canadian Press. His radio news stories have been aired via Broadcast News to radio stations around the country. Bruce is a five-time Ontario Newspaper Award finalist for news reporting and opinion and analysis writing. A Humber College Print and Broadcast Journalism graduate, Bruce spent more than a decade in the Kawartha Lakes region of Ontario before moving to Chatham-Kent in 2001.
« Treaties Recognition Week 15th Christmas House Tour focuses on Victoria Ave. area »
71 Sass Rd.,
Chatham, Ontario
N7M 5J4
Follow @chathamvoice
Come On Get Social...
© 2018, C-K Media Inc.
Designed by Hub Creative Group | Powered by WP Momentum


With experts warning that hacking voting systems is extremely easy and early voters reporting that their presidential ballots aren't being properly tallied, a growing number of Americans are losing faith the in the legitimacy of the nation's election process.
The Brookings Institution and PRRI on Tuesday revealed polling data showing that a dismal 43 percent of Americans have faith in the nation's voting system ahead of one of the most contentious presidential elections in decades.
Fewer than half (43%) of the public say they have a great deal of confidence that their vote will be counted accurately. Roughly four in ten (38%) Americans report having only some confidence, while close to one in five (17%) say they have little confidence their vote will be accurately counted. There are stark differences among likely voters, with 70% of Clinton supporters—but only 41% of Trump supporters—reporting a great deal of confidence their votes will be counted accurately.
Americans are almost evenly divided over what constitutes the more significant problem with U.S. elections today: People casting votes who are not eligible (37%) or eligible voters being denied the right to vote (41%). Roughly one in ten (9%) Americans volunteer that voter apathy is the most significant problem.
Roughly two-thirds (66%) of Republicans believe voter fraud is a bigger problem than voter disenfranchisement, compared to only 19% of Democrats. More than six in ten (62%) Democrats say eligible voters being denied access is the bigger problem facing the election system.
A majority (57%) of Americans agree politics and elections are controlled by people with money and by big corporations so it doesn't matter if they vote, compared to roughly four in ten (42%) who disagree.
And while Democrats are quick to suggest that the voter concerns are mere paranoia provoked by remarks coming from the Trump campaign, a growing number of social media users are reporting having trouble casting ballots for Donald Trump in areas where early voting is underway.
There are also multiple warnings of vote-switching from users on a pro-Trump page on Reddit.